סמינר מכוני AI בנושא: Quantum maximum likelihood prediction via Hilbert space embeddings

Abstract: Maximum likelihood prediction plays a major (hidden) role in modern large language models via the next token prediction task. In this talk, we propose and study a simplified version, based on an i.i.d. data model. The model is based on a quantum maximum likelihood predictor, which is obtained by embedding empirical distributions into quantum states and minimizing quantum relative entropy over a prescribed model class. We interpret this predictor via quantum reverse information projection and a quantum Pythagorean theorem, under structural assumptions such as unitary invariance and closure under pinching. We extend this theorem to non-self-adjoint mixture families in finite dimensions and establish a related infinite-dimensional inequality under additional regularity conditions. Finally, we present non-asymptotic guarantees, including convergence rates and concentration inequalities in trace norm and quantum relative entropy. Joint work with Sreejith Sreekumar. Bio: Nir Weinberger is an Associate Professor at the The Viterbi Faculty of Electrical and Computer Engineering, Technion - Israel Institute of Technology. Previously, from 2017 to 2018 he was a post-doctoral fellow at Tel-Aviv University, and from 2018-2020 he was a Technion-MIT post-doctoral fellow at the Massachusetts Institute of Technology, Cambridge, MA, USA. He has received the B.Sc. and M.Sc. degrees from Tel-Aviv University, Tel-Aviv, Israel, in 2006 and 2009, respectively, and his Ph.D. degree in 2017, from the Technion, Israel Institute of Technology. Previously, he also worked as an algorithm Engineer, specializing in Digital Communications and Signal Processing.